A process for treating a semiconductor wafer (e.g., a silicon wafer) used for a semiconductor includes controlling an in-plane temperature distribution of the semiconductor wafer as desired while controlling a temperature of the semiconductor wafer to a temperature setpoint.
Accordingly, the temperature of the semiconductor wafer is typically controlled to a desired temperature by providing a plurality of temperature adjusters and control loops to the respective temperature adjusters and independently controlling the temperature adjusters with the control loops. As one of such multi-input multi-output control methods, a model following servo control method is used.
The model following servo control method includes: selecting a model (e.g., a second-order lag system) having dynamic characteristics generally desired as a reference model; and providing a setpoint response to make a control variable to follow a step response of the reference model as a reference trajectory.
In order to improve a throughput in the process, it is desirable to intentionally saturate the manipulated variable to reach a setpoint at the maximum speed in the shortest time.
Patent Literature 1 (JP2016-12228A) discloses a technology of generating a reference model based on a response in which, in a plurality of control loops, a manipulated variable of a first control loop having the slowest response speed is defined as 100% and the rest of the control loops is controlled to follow the first control loop; with use of the generated reference model, searching for a manipulated variable pattern, using a predetermined evaluation function, for reaching the temperature setpoint in the shortest time; giving a manipulated variable of the searched optimal manipulated variable pattern to the reference model to obtain an output; and using the obtained output as a reference model output.
In the technology of Patent Literature 1, a single reference model is generated based on the dynamic characteristics in heating to provide the reference model output to be followed.
However, in a thermo-module such as Peltier element, the dynamic characteristics sometimes differ in heating and cooling. Since the dynamic characteristics in the heating exhibit a larger output, when the reference model output for the heating is used in the cooling, the reference model output precedes an actual output, so that uniformity cannot be kept.
When the reference model output for the cooling is used, the response speed becomes slow although the uniformity is ensured.